April - 1 May, GNSS Derived TEC Data Calibration

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1 Workshop on Science Applications of GNSS in Developing Countries (11-27 April), followed by the: Seminar on Development and Use of the Ionospheric NeQuick Model (30 April-1 May) 11 April - 1 May, 2012 GNSS Derived TEC Data Calibration CIRAOLO Luigi Consiglio Nazionale delle Ricerche Istituto di Fisica Applicata "Carrara" via Madonna del Piano Sesto Fiorentino ITALY

2 TEC calibration technique tests using model simulated data: L. Ciraolo IFAC-CNR, Firenze / ICTP, Trieste l.ciraolo@ifac.cnr.it, lciraolo@ictp.it Seminar on Development and Use of the Ionospheric NeQuick Model Trieste, 30 April-1 May 2012

3 How accuracy of calibration techniques can be estimated Examination of residuals after a calibration run Res ijt = S ijt - Σ n c t n p n ( l ijt, f ijt ) sec χ ijt - Ω Arc will provide with useful information about the Internal consistency of the solution Residuals are plotted in the following examples for few sample stations. Standard deviation of the individual samples is reported. Reminder S ijt Σ n c t n p n ( l ijt, f ijt ) sec χ ijt sec χ ijt Ω Arc the observations the expansion of Vertical (Equivalent) TEC the mapping function the unknown arc offset

4 Internal consistency of the method is estimated from the residuals (actual data) Res ijt = S ijt - Σ n c t n p n ( l ijt, f ijt ) sec χ ijt - Ω Arc

5 Residuals, actual data

6 Residuals, actual data

7 Residuals, actual data

8 Sigma of the shown sample residuals ranges from.5 to 4 TECu according to latitude. Is this an estimation of the accuracy of the calibration? No, as this requires a comparison with truth data, which are unavailable (Incoherent Scatter Radar, Radar Altimeter may help, but are not sufficient). What can look more like truth data? Artificial data produced by Ionospheric Models. But keeping in mind that agreement with artificial data is a condition necessary but not sufficient to validate the method

9 The artificial data Ionospheric models enable to estimate median electron density at some time at some geographic location, i.e. given date and time, latitude, longitude, height. N e = N e (t,φ,λ,h) TEC is the integral of electron density along the ray-path from satellite to receiver, which will be numerically evaluated as the sum TEC = Ne ( P) ds TEC N e (P i )δs i or with any more effective numerical algorithm (Gauss, )

10 Model TEC computation TEC = N ( P) ds e N e (P i )δs i Divide the path in elements δs i At each point P i compute the electron density N e (P i ) provided by the model Multiply by the element length δs i Cumulate all elements Sat Rx P i, ds i P i, point on the generic i th shell δs i increment in arc length

11 Simple uses of artificial data: the mapping function Which errors do affect the standard approach (actual vertical TEC) of mapping function? Using an artificial ionosphere: Compute χ Compute Slant S Compute Vertical TEC V at the Ionospheric Point Error: S V sec χ Vertical Plot Error distribution dh P χ ds To GPS Station h Ionosphere

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14 Simple uses of artificial data: VEC and VEq In the Single-Station / Arc Offset calibration the Vertical Equivalent TEC VEq for which it is exactly S = VEq sec χ is used. How different is VEq from actual Vertical TEC (VEC)? Using an artificial ionosphere: By definition Compute χ Compute Slant S VEq = S cos χ Compute Vertical TEC V at the Ionospheric Point VEC Plot VEC, VEq Plasmasphere can be included too using a suitable model

15 Integration paths for S VEC VEC VEq = S cos χ Rx P χ S Sat h Ref

16 Simple uses of artificial data: How much VEC and VEq differ?

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20 Test of Single-Station, Arc-Offset solution Generation of artificial truth data Given all slants actually observed and archived in a (quasi) complete set of IGS stations ( 200 per day) for year 2000 for days ( March 28-31) Re-compute them using NeQuick (Az =150), integrating up to 2000 km Therefore: Not only the actual GPS constellation has been preserved for the reference period, but also the possible lack of observations (this will affect the solution)

21 Internal consistency: Residuals, simulated data Res ijt = S ijt - Σ n c t n p n ( l ijt, f ijt ) sec χ ijt - Ω Arc

22 Testing the calibration procedure Set of slants from IGS Recompute using NeQuick Truth Data S IN Arrange slants by arcs Correct for phase jumps Level Arc Evaluate Arc Offsets Compute S Out S Out -S In

23 S Out S In are plotted vs time Worth (but expected) noting that errors at low latitudes are larger Remark about highlighted arc: errors show a weakness of the solution. These errors occur for arcs of low elevation also if, in some case, of long duration. Processing real data, there is no chance to know if the subject arc is ill-calibrated (unless in presence of very strong errors) Testing the solution with simulated data will (likely) enable to find a more effective way of avoiding such errors, or in a last instance, rejecting them

24 Slant Out -Slant In, TECu

25 Slant Out -Slant In, TECu

26 Slant Out -Slant In, TECu

27 Slant Out -Slant In, TECu

28 An overall look to the errors: S Out S In, whole set

29 An overall look to the errors: S Out S In, probability density 0.12% < % > 10

30 Error s behavior vs latitude: percentiles, whole set

31 Simulation: role of multi-path contribution λ An arbitrary set of satellite + receiver biases + multipath errors is added to model slants Station bias γ = 25 Satellite biases β i = 10 * (Rnd() - Rnd()), i=1,..,32 LevelingError λ Arc = 10 * Rnd() Arc Offset Ω Arc = 1000 * Rnd() Arc =1.. Number of Arcs NextData are processed both by traditional and arc offset single-station calibration.

32 Set of slants from IGS Recompute using NeQuick Truth Data S IN ( VEq ) Arrange slants by arcs Correct for phase jumps Add biases β + γ + λ Level Arcs Evaluate Traditional/ Arc Offsets Compute S Out, VEq S Out -S In

33 Traditional, SOut - SIn

34 Traditional, VEq computed / VEq True

35 Arc Offset, SOut - SIn

36 Arc Offset, VEq computed / VEq True

37 Thank you

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